Brouwer's theorem

Brouwer's theorem

[′brau̇·ərz ‚thir·əm]
(mathematics)
A fixed-point theorem stating that for any continuous mapping ƒ of the solid n-sphere into itself there is a point x such that ƒ(x) = x.
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References in periodicals archive ?
On the other hand, however, Sperner's lemma which is used to prove Brouwer's theorem can be constructively proved.
By applying Brouwer's Theorem we can immediately speculate about the existence of a point x such that k(x) = x: (2)
0]) take on sets of values, as in the Kukutani fixed point theorem, which generalizes Brouwer's theorem to a point-to-set mapping.